48 ideas
21757 | Philosophy is the conceptual essence of the shape of history [Hegel] |
5278 | Philosophy is no more than abstractions concerning observations of human historical development [Marx/Engels] |
22289 | Dedekind proved definition by recursion, and thus proved the basic laws of arithmetic [Dedekind, by Potter] |
10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
22288 | We have the idea of self, and an idea of that idea, and so on, so infinite ideas are available [Dedekind, by Potter] |
10706 | Dedekind originally thought more in terms of mereology than of sets [Dedekind, by Potter] |
9823 | Numbers are free creations of the human mind, to understand differences [Dedekind] |
10090 | Dedekind defined the integers, rationals and reals in terms of just the natural numbers [Dedekind, by George/Velleman] |
17452 | Ordinals can define cardinals, as the smallest ordinal that maps the set [Dedekind, by Heck] |
7524 | Order, not quantity, is central to defining numbers [Dedekind, by Monk] |
14131 | Dedekind's ordinals are just members of any progression whatever [Dedekind, by Russell] |
14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil [Dedekind, by Russell] |
18094 | Dedekind says each cut matches a real; logicists say the cuts are the reals [Dedekind, by Bostock] |
9824 | In counting we see the human ability to relate, correspond and represent [Dedekind] |
9826 | A system S is said to be infinite when it is similar to a proper part of itself [Dedekind] |
13508 | Dedekind gives a base number which isn't a successor, then adds successors and induction [Dedekind, by Hart,WD] |
18096 | Zero is a member, and all successors; numbers are the intersection of sets satisfying this [Dedekind, by Bostock] |
18841 | Categoricity implies that Dedekind has characterised the numbers, because it has one domain [Rumfitt on Dedekind] |
14130 | Induction is proved in Dedekind, an axiom in Peano; the latter seems simpler and clearer [Dedekind, by Russell] |
8924 | Dedekind originated the structuralist conception of mathematics [Dedekind, by MacBride] |
9153 | Dedekindian abstraction talks of 'positions', where Cantorian abstraction talks of similar objects [Dedekind, by Fine,K] |
5287 | Philosophical problems are resolved into empirical facts [Marx/Engels] |
9825 | A thing is completely determined by all that can be thought concerning it [Dedekind] |
23872 | 'Society determines consciousness' is contradictory; society only exists in minds [Weil on Marx/Engels] |
5277 | Life is not determined by consciousness, but consciousness by life [Marx/Engels] |
9189 | Dedekind said numbers were abstracted from systems of objects, leaving only their position [Dedekind, by Dummett] |
9827 | We derive the natural numbers, by neglecting everything of a system except distinctness and order [Dedekind] |
9979 | Dedekind has a conception of abstraction which is not psychologistic [Dedekind, by Tait] |
5280 | Language co-exists with consciousness, and makes it social [Marx/Engels] |
5276 | The nature of an individual coincides with what they produce and how they produce it [Marx/Engels] |
5281 | Consciousness is a social product [Marx/Engels] |
5289 | When aristocracy or the bourgeoisie dominate, certain values dominate with them [Marx/Engels] |
5274 | Young Hegelians proposed changing our present consciousness for liberating critical consciousness [Marx/Engels] |
21992 | Producing their own subsistence distinguishes men from animals [Marx/Engels] |
5275 | Men distinguish themselves from animals when they begin to produce their means of subsistence [Marx/Engels] |
5292 | Individuals are mutually hostile unless they group together in competition with other groups [Marx/Engels] |
5293 | Only in community are people able to cultivate their gifts, and therefore be free [Marx/Engels] |
5273 | Young Hegelians think consciousness is chains for men, where old Hegelians think it the bond of society [Marx/Engels] |
5283 | In communist society we are not trapped in one activity, but can act freely [Marx/Engels] |
5282 | If the common interest imposes on the individual, his actions become alienated and enslaving [Marx/Engels] |
5288 | The class controlling material production also controls mental production [Marx/Engels] |
5290 | The revolutionary class is opposed to 'class', and represents all of society [Marx/Engels] |
5294 | To assert themselves as individuals, the proletarians must overthrow the State [Marx/Engels] |
5285 | Slavery cannot be abolished without the steam-engine [Marx/Engels] |
5284 | Communism abolishes private property and dissolves the powerful world market [Marx/Engels] |
5291 | The law says private property is the result of the general will [Marx/Engels] |
5279 | Human history must always be studied in relation to industry and exchange [Marx/Engels] |
5286 | Most historians are trapped in the illusions of their own epoch [Marx/Engels] |